The National Theatre’s promotional campaign for Simon Godwin’s new Twelfth Night has been all Tamsin Greig, all the time.

The video trailer and the programme design devote themselves entirely to showing off the film and TV star, who also won an Olivier Award in 2007 for the Royal Shakespeare Company’s Much Ado About Nothing, and here plays Shakespeare’s stern steward Malvolio – now Malvolia.

Betting the farm on one actor (in a role that is usually featured but not necessarily starring) could be a risk, but this one’s a bet worth taking: Greig turns in a glorious gender-bending performance in this all-around stellar production of Shakespeare’s most gender-bending play.

Godwin and designer Soutra Gilmour make tremendous use of the Olivier Theatre’s stage. One dominated by a magical revolving staircase that rotates and rotates, revealing a seemingly bottomless offering of new locations – a gym, a garden, two mansions, a spa, a hospital, a church, you name it.

The production’s unabashed updating of the play’s setting (there’s a car, a motorbike, and an intercom system in the opening two minutes) is illuminating rather than invasive, due to the company’s meticulous and celebratory engagement with the text. In one giddy moment of textual play, the Countess Olivia asks Viola, in disguise as Cesario, “Would you undertake another suit?” while holding out a Speedo to her. (Godwin’s apparently endless inventiveness does seem to be reaching its far limits by the time, late in the production, that we arrive at a drag queen singing the “To be or not to be” speech in a gay bar.)

Looming larger and shining more brightly than the gilded set, though, is Greig’s dazzling Malvolia, who transforms from Mrs. Danvers-like austerity into a galloping bundle of joy when she (mistakenly) believes that Olivia, whom she serves, returns her love. In the tour de force garden scene, in which Malvolia reads Olivia’s purported love letter, forged by the crafty Maria (Niky Wardley), Malvolia’s jubilation bubbles over the fourth wall, leading to some uproarious engagement with the audience. Greig’s layered performance renders the audience at once participatory in Malvolia’s joy and complicit in her eventual humiliation.

Watch the full-bodied dexterity with which Greig leaps over a doorframe to receive Olivia’s orders or encircles Sir Andrew, wordlessly chastising him for his frivolity, before sweeping out of the room. Greig as Malvolia seems both impossibly fortuitous and deliciously inevitable.

Tamara Lawrance as Viola, Phoebe Fox as Olivia, image by Marc Brenner

Godwin has assembled a knockout cast, but they largely fade into the background in the wake of Greig’s monumental Malvolia. The central love triangle – Viola (Tamara Lawrance) loves Orsino (Oliver Chris) who loves Olivia (Phoebe Fox) who loves Cesario (actually Viola) – seems unusually incidental. Lawrance is a charming Viola, endearingly dumbfounded by the situations her disguise leads her into. But the suggestion that Viola may, on some level, reciprocate Olivia’s interest mutes rather than enhances the crisp tensions of their scenes together.

Fox’s Olivia is very silly, rather petulant, and slightly mad. Chris handles the verse neatly, but his Orsino makes minimal impact amongst his madcap companions. Daniel Ezra portrays a movingly conflicted Sebastian, Viola’s twin brother. Tim McMullan’s Sir Toby Belch and Daniel Rigby’s Sir Andrew Aguecheek are ridiculously delightful in their partying, and in their machinations against Malvolia, while Doon Mackichan’s boisterous Feste sings the play’s several songs feelingly.

Twelfth Night is probably Shakespeare’s most musical play (from “If music be the food of love” onwards) and Michael Bruce’s joyous jazzy Latin underscoring is a highlight. Onstage musicians, including the superb Hannah Lawrence on saxophone, clarinet, and flute, have some inventive interactions with the actors. Olivia and Sir Andrew both have a penchant for breaking out into amusing bite-size dances whenever they hear music play.

To Godwin’s credit, he recognizes that casting Greig as Malvolia has consequences, and he does not shy away from the undercurrents of the homophobia that now seems, in part, to motivate Sir Toby and his co-conspirators. The choice to cast Sir Toby, Sir Andrew, and Maria all about a generation younger than they appear in most productions increases the sense that their antipathies towards Malvolia are more instinctive than age-old.

Even as the central pairs of lovers test the boundaries of their own sexualities, and all four (Olivia, Orsino, Viola, and Sebastian) exhibit complicated desires throughout the production, there is never a sense that the surety of their eventual heterosexual unions has been threatened. No such safety net exists for Malvolia, and Godwin and Greig embrace the softly tragic isolation that Malvolia experiences at the play’s end: the pathos of her brief imprisonment positions her as closer to Richard II than any comic character.

The play’s final image is not, unlike most of this production, particularly funny, but it feels at once entirely true to Shakespeare and bruisingly relevant.

Twelfth Night is playing at the Olivier Theatre until 13 May. For more information and tickets, see nationaltheatre.org.uk.